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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 16 — Aug. 11, 2014
  • pp: 19327–19336
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Quantitatively assessing flow velocity by the slope of the inverse square of the contrast values versus camera exposure time

Jialin Liu, Hongchao Zhang, Zhonghua Shen, Jian Lu, and Xiaowu Ni  »View Author Affiliations


Optics Express, Vol. 22, Issue 16, pp. 19327-19336 (2014)
http://dx.doi.org/10.1364/OE.22.019327


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Abstract

The slope of the inverse square of the contrast values versus camera exposure time at multi-exposure speckle imaging (MESI) can be a new indicator of flow velocity. The slope is linear as the diffuse coefficient in Brownian motion diffusion model and the mean velocity in ballistic motion model. Combining diffuse speckle contrast analysis (DSCA) and MESI, we demonstrate theoretically and experimentally that the flow velocity can be obtained from this slope. The calculation results processes of the slop don’t need tedious Newtonian iterative method and are computationally inexpensive. The new indicator can play an important role in quantitatively assessing tissue blood flow velocity.

© 2014 Optical Society of America

1. Introduction

Laser speckle contrast analysis (LASCA) [1

1. A. Fercher and J. Briers, “Flow visualizaiton by means of single-exposure speckle photography,” Opt. Commun. 37(5), 326–330 (1981). [CrossRef]

, 2

2. J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1(2), 174–179 (1996). [CrossRef] [PubMed]

], firstly introduced in the 1980s, is a particularly attractive method because of its simple and inexpensive manner. It has been widely used to image biological blood flow [3

3. P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett. 31(12), 1824–1826 (2006). [CrossRef] [PubMed]

5

5. Z. Wang, S. Hughes, S. Dayasundara, and R. S. Menon, “Theoretical and experimental optimization of laser speckle contrast imaging for high specificity to brain microcirculation,” J. Cereb. Blood Flow Metab. 27(2), 258–269 (2007). [CrossRef] [PubMed]

]. The very essence [6

6. R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005). [CrossRef]

] of LASCA is to quantify the visibility of the speckle pattern in terms of moments of the distribution of recorded intensities for a given exposure duration. The visibility of the speckle pattern is defined as the ratio of the standard deviation to the mean intensity,Ks=σs/I, where the subscript s refers to the spatial or to temporal [3

3. P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett. 31(12), 1824–1826 (2006). [CrossRef] [PubMed]

, 7

7. H. Cheng, Y. Yan, and T. Q. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express 16(14), 10214–10219 (2008). [CrossRef] [PubMed]

].

LASCA is mostly based on single scattering, which is limited on a superficial layer inside a relatively transparent medium. Diffuse speckle contrast analysis (DSCA) [8

8. R. Bi, J. Dong, and K. Lee, “Deep tissue flowmetry based on diffuse speckle contrast analysis,” Opt. Lett. 38(9), 1401–1403 (2013). [CrossRef] [PubMed]

, 9

9. R. Bi, J. Dong, and K. Lee, “Multi-channel deep tissue flowmetry based on temporal diffuse speckle contrast analysis,” Opt. Express 21(19), 22854–22861 (2013). [CrossRef] [PubMed]

] exploits the diffusive nature of the transport of light for the relatively turbid medium which exhibits strong multiple scattering. This new technique is formed by the union of diffusing wave spectroscopy (DWS) [10

10. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988). [CrossRef] [PubMed]

] and LASCA. The autocorrelation function of DSCA can be obtained from the correlation transport equation, which considers the effects of absorption, scattering and different dynamical motions and the influence of boundaries and heterogeneities in this physical model. Thus by means of this autocorrelation function, we can obtain quantitative determination of dynamical properties of the medium. DSCA has more advantages and can overcome some difficulties emerging from LASCA.

In this paper, we present a new indicator for the flow index, i.e. the slope of 1/K2 vs. camera exposure time (T) at multi-exposure speckle imaging (MESI) [14

14. A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008). [CrossRef] [PubMed]

]. It is theoretically derived that the slope of the function of 1/K2 vs. T (kslope) changing over exposure time depends on source-detector distance, flow information and optical parameters of medium (the absorption coefficient μa, the scattering coefficient μs and anisotropy parameter g et al.). When the ratio of the minimum exposure time to the correlation time is much more than 1, kslope is in linear relationship with the diffuse coefficient (DB) in Brownian motion diffusion model and the mean velocity (v) in ballistic model (random flow and shear flow [15

15. X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, and D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B 7(1), 15–20 (1990). [CrossRef]

]). We perform a tissue phantom experiment in multiple scattering slab medium and Monte Carlo simulation to demonstrate this linear relationship between this new indicator and the mean velocity. The experiment results and MC simulation results fit well. kslope can become a quantitative indicator for tissue blood flow velocity. The new indicator has more advantages and can play an important role in quantitatively assessing tissue blood flow velocity.

2. Theory

2.1 Diffuse speckle contrast analysis

In homogeneous multiple scattering slab medium, the electric field autocorrelation function G1(r,τ)=E(r,t)E*(r,t+τ) can be obtained from the correlation diffusion equation [16

16. D. Boas and A. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A 14(1), 192–215 (1997). [CrossRef]

]
[-13μs'2+μa+13μs'k02Δr2(τ)]G1(r,τ)=S(r)
(1)
where, μs'=μs(1g) is reduced scattering coefficient, k0 is the wavenumber of the light in medium, S(r) is the light-source distribution and Δr2(τ) represents the mean square displacement of the moving scatterers after a delay time τ.

When the slab thickness [17

17. Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, and P. Sheng, “Wave transport in random media: The ballistic to diffusive transition,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(4), 4843–4850 (1999). [CrossRef] [PubMed]

] is d/ltr3, the unnormalized electric autocorrelation function has the following expression [18

18. T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010). [CrossRef]

] by standard diffusion approximation,
G1(r,z,τ)=3μs'4πm=(exp(k(τ)r+,m)r+,mexp(k(τ)r,m)r,m)
(2)
r±,m=r2+(zz±,m)2
(3)
z+,m=2m(d+2zb)+ltr
(4)
z,m=2m(d+2zb)2zbltr
(5)
zb=2(1Reff)/3μs'(1+Reff)
(6)
Reff1.44n2+0.71n1+0.668+0.00636n
(7)
ltr=1μs'
(8)
k(τ)=3μs'μa+αμs'2k02Δr2(τ)
(9)
where, d is the thickness of slab medium, ltr is the transport mean free path, Reff is effective reflection coefficient to account for the index mismatch between media and surrounding medium, n = nin/nout is the ratio of the index of refraction inside and outside the diffusing medium,α is the fraction of dynamic photon scattering events in medium, m is an integer, r is source-detector distance in x-y plane and z is along the thickness direction of slab medium. A scheme of the geometry together with a description of some of the notations is shown in Fig. 1.
Fig. 1 Slab geometry and some notations.

Substituting Eqs. (2)(10) into Eq. (11), the diffuse speckle contrast can be written as
K2(T)=2βT0T(1τ/T)m=x=ξ±m,±x[exp(12(r±,m+r±,x)μs'k0Δr2(τ))]2dτ
(12)
where ξ ± m, ± x is constant at the fixed source-detector distance and depends on r ± m, r ± x and G1(r, z, 0).

For Brownian motion Δr2(τ)=6DBτ, g1(r,z,τ)is the sum of the similar function form g1(τ)=exp(Γτ), correspond to contrast function form [6

6. R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005). [CrossRef]

]

VB(T)=β[(3+6ΓBT+4ΓBT)e2ΓBT3+2ΓBT]/(2ΓB2T2)
(13)
ΓB=32(r±,m+r±,x)2μs'2k02DB
(14)

For the ballistic motion model Δr2(τ)=v2τ2, g1(r,z,τ) is the sum of the similar function form g1(τ)=exp(Γτ), correspond to contrast function form [6

6. R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005). [CrossRef]

]

Vb(T)=β[e2ΓbT1+2ΓbT]/(2Γb2T2)
(15)
Γb=12(r±,m+r±,x)μs'k0v
(16)

When the ratio of the exposure time to the correlation time is much more than 1, i.e. ΓBT1 and ΓbT1, the numerator function (3+6ΓBT+4ΓBT)e2ΓBT and e2ΓbT can be omitted in Eq. (13) and Eq. (15). V(T) of Brownian motion and ballistic motion can be simplified to the same following expression

VB(T)=β(2ΓBT3)/(2ΓB2T2)
(17)
Vb(T)=β(2ΓbT1)/(2Γb2T2)
(18)

Exploiting the simplified Eq. (17) and Eq. (18), the inverse square of the contrast values 1/K2(T) is given by

βKB2(T)=T2Γ1T32Γ2=1Γ1T+12Γ123Γ2Γ1T
(19)
Γ1=m=x=ξ±m,±x1ΓB=23DBμs'2k02m=x=ξ±m,±x1(r±,m+r±,x)2
(20)
Γ2=m=x=ξ±m,±x1ΓB2=49DB2μs'4k04m=x=ξ±m,±x1(r±,m+r±,x)4
(21)
βKb2(T)=T2Γ3T12Γ4=1Γ3T+12Γ32Γ4Γ3T
(22)
Γ3=m=x=ξ±m,±x1Γb=2μs'k0vm=x=ξ±m,±x1(r±,m+r±,x)
(23)
Γ4=m=x=ξ±m,±x1Γb2=4μs'2k02v2m=x=ξ±m,±x1(r±,m+r±,x)2
(24)

Because of Γ1/T1 and Γ3/T1, Eq. (19) and Eq. (22) can be simplified to the following expression

1KB2(T)=1β(1Γ1T+3Γ22Γ12)=1β(DB3μs'2k022m=x=ξ±m,±x1(r±,m+r±,x)2T+m=x=ξ±m,±x1(r±,m+r±,x)4(m=x=ξ±m,±x1(r±,m+r±,x)2)2)
(25)
1Kb2(T)=1β(1Γ3T+Γ42Γ32)=1β(vμs'k02m=x=ξ±m,±x1(r±,m+r±,x)T+m=x=ξ±m,±x1(r±,m+r±,x)2(m=x=ξ±m,±x1(r±,m+r±,x))2)
(26)

From the above results, we can deduce that the function of 1/K2(T) has a linear relationship with T for Brownian motion and ballistic motion over a broad range. The slope of the function of 1/K2(T) vs T (kslope) depends on the source-detector distance, flow information and optical parameters of medium. When the source-detector distance is constant, kslope has a linear relationship with diffuse coefficient DB in Brownian motion and mean velocity v in ballistic motion. kslope can be used as the new indicator for quantitatively assessing flow index.

2.2 Monte Carlo simulation

For checking the accuracy of the theory, we ran simulation for a point source vertically entering the slab medium with different dynamical properties. For our simulation, one hundred million is applied and the code takes ~2 h to run on an Intel i5 3450 3.1 GHz processer. The well-developed MC codes [19

19. L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995). [CrossRef] [PubMed]

, 20

20. L. Wang and S. L. Jacques, http://omlc.ogi.edu/software/mc/.

] have been widely used to simulate light transport in tissues. We modify these codes to be able to obtain the momentum transfer of each photon-scatter collision and finally success to record the numerical distribution of total dimensionless momentum transfer. The normalized autocorrelation can be calculated as
g1(τ,z,r)=0P(Y,r,z)exp[13k02Δr2(τ)Y]dY
(27)
where, P(Y, r, z) is normalized probability density function of total dimensionless momentum transfer at different distances and Y=i=1n(1cosθi) is the total dimensionless momentum transfer experienced n uncorrelated scattering events. The contrast can be calculated by Eq. (11). The whole calculation process avoids the standard diffusion approximation.

Figure 2(a) shows MC simulation results and the analytical results Eq. (26) when the mean velocity is 0.80 mm/s.
Fig. 2 (a) Comparison between Monte Carlo simulation and standard diffusion approximation results Eq. (26) for the inverse square of the contrast values at different exposure times. The black spot-line corresponds to the MC simulation results and other spot-lines correspond to Eq. (26) results; (b) Normalized probability density function of total dimensionless momentum transfer at the position r = 0.2 cm and z = 2.0 cm. The mean velocity is 0.80 mm/s. μs = 2cm−1, μa = 0.01cm−1, λ = 632.8nm and d = 2cm.
We try much larger m values to calculate Eq. (26). When m tends to be infinite, the inverse square of the contrast values change very slowly and are almost constant. The slope difference between m = 0, ± 1,…, ± 30 and m = 0, ± 1,…, ± 300 is 0.3%. However, a systematic difference remains between the analytical expressions and MC simulation results. This small discrepancy is caused by the photons which don’t experience enough scattering events and are non-diffuse after passing through the slab. As shown in Fig. 2(b) the single scattering photons and the ballistic-diffusive transition photons account for a certain proportion, which make 1/K2(T) become smaller than the analytical values calculated by diffusion approximation. However, we can clearly find that the functions of 1/K2(T) both have a linear relationship with T for ballistic motion over a broad range.

3. Experimental set-up

To validate the role of the new indicator, a flow phantom was built as shown by Fig. 3.
Fig. 3 Schematic of the experimental setup using flow phantom.
The continuous He-Ne laser source (Melles Griot 25-LHP-925-230; λ = 632.8nm, 30mW, Carlsbad California, USA) with a long coherence length is vertically entering the rectangular vessel (2cm height and d = 2cm wide in cross section). The intralipid solution with a concentration of 0.15% is pumped through the polyethylene tubing (4.8mm inner diameter), at different mean flow velocities and different exposure times. The optical properties of the flow phantom are μs = 2cm−1 and μa = 0.01cm−1, which satisfy μs >> μa, and the diffusion approximation is valid.

The mean flow velocities are 0.80 mm/s to 2.40 mm/s, drived by a digital peristaltic pump. The exposure time is set at 0.3 ms, 0.5 ms, 0.8 ms, 1 ms, 2 ms and 3 ms. The transmission speckle is imaged using a prime lens, 120mm lens tube and a CCD (Microvision MV-VS141FM/C; 12 bits, pixel size 4.65 μm*4.65 μm, resolution ratio 1392*1040). The imaging system has a magnification of 1.7. The detector position is set at the position z = 2.0 cm r = 0.2 cm.

4. Results and discussion

20 raw speckle images are recorded for each mean velocity and each exposure time. Because of the influence of the CCD background noise, the raw speckle images need to subtract the average noise intensity, which is averaged over 50 noise images recorded for each exposure time, before the calculation of the spatial contrast value Ks. Ks is calculated from every segment of 101 × 101 pixels for reducing the noise in laser speckle correlation [12

12. S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express 18(14), 14519–14534 (2010). [CrossRef] [PubMed]

]. 20 speckle contrast images Ks are averaged for each exposure time and each mean velocity.

Figure 4 shows the spatial contrast of different mean velocities at different exposure times.
Fig. 4 Spatial contrast of different mean velocities at different exposure times.
The mean velocities are 0.80 mm/s, 1.60 mm/s and 2.40 mm/s corresponding to the black, the red and the blue curves respectively. If we expect to obtain the linear relationship in correlation time τc, we need nonlinearly fit the contrast by MESI equation. However, β is one of the unknown quantities and mainly depends on the experiment conditions. Usually we obtain β by calculating the contrast of the reflectance static speckle. Holding β constant, we make the nonlinear fitting to obtain τc. This calculation processes need tedious Newtonian iterative method and are computationally inexpensive. Meanwhile, to improve the signal to noise ratio (SNR), the number of exposure time must be adequate. This process is cumbersome.

The new indicator kslope can overcome these shortcomings as motioned above. As shown in Fig. 5, we can clearly see that the experiment results and the analytical results have the same tendency.
Fig. 5 Inverse square of the contrast values of different mean velocities at different exposure times. The solid line corresponds to the analytical results Eq. (26) and the spot corresponds to the experiment results. The mean velocities are respectively 0.8 mm/s, 1.20 mm/s and 1.60 mm/s. The deviation error bars are shown for the data.
Both 1/Ks2(T) have a linear relationship with T at different mean velocity. The difference mainly caused by β is at the slope as shown in Eqs. (25) and (26). The unpolarized recorded speckle images and the reduction in the measured contrast due to averaging over uncorrelated speckles make β < 1. The kslope of the experiment results is equivalent to enlarge 1/β times. Nevertheless, we don’t need consider the influence of β and don’t calculate its value like the calculation process in MESI, because the effect of β is same for different velocities. Meanwhile, the linear fitting is relatively simple and doesn’t need too much exposure times for achieving the same SNR. The new indicator has more advantages than the correlation time τc.

In order to verify our argument on the analytical expressions Eq. (26), we calculate experiment results kslope at different mean velocities as shown in Table 1and Fig. 6(a).

Table 1. Normalized values of experiment results and analytical results kslope at different mean velocities

table-icon
View This Table
Fig. 6 (a) Experiment results kslope versus mean flow velocity and (b) normalized values of experiment results and the analytical results Eq. (26) kslope versus normalized mean flow velocity. The velocity 1.60 mm/s is baseline speed. The slope of baseline speed is baseline measure value. The deviation error bars are shown for the data.
We can clearly find that kslope varies linearly with the scattering particle flow velocity. For eliminating the influence of β and plotting on the same scale in an image, the normalization is performed with respect to kslope of the experiment results and the analytical results at their respective median values as shown in Table 1. The normalization process is performed for the different mean velocities in the same way to observe easily this linear relationship between the slope and the mean velocity.

Figure 6(b) shows that the normalized kslope of experiment results and the analytical results fit well. The median mean velocity can be regarded as the baseline measure value, so we can utilize this linear relationship to obtain other quantitative velocity information. kslope can be a new indicator to quantitatively assesse flow velocity.

5. Conclusion

In this work, we have presented a new indicator kslope to measure quantitatively mean velocity. The calculation theory is based on diffuse speckle contrast analysis (DSCA) and multi-exposure speckle imaging (MESI). We demonstrate that we are able to use the linear relation to fit the inverse square of the contrast values (1/K2) at different exposure times. kslope is in linear relationship with the mean velocity. We provide MC simulation results and experiment results in a liquid phantom with varying flow velocity in the transmission geometry. The results are in support of our theory.

We can utilize this linear relationship and the baseline measure value kslope of known mean velocity to obtain other quantitative velocity information. Meanwhile the calculation process of kslope doesn’t need consider the influence of the unpolarized recorded speckle images and the reduction in the measured contrast due to averaging over uncorrelated speckles. The normalization can be performed to overcome these influence as motioned above. The computation can be greatly simplified for multi-exposure speckle imaging. The new indicator can play an important role in quantitatively assessing tissue blood flow velocity.

Acknowledgment

The work is supported by the National Natural Science Foundation of China under Grant No 11174151.

References and links

1.

A. Fercher and J. Briers, “Flow visualizaiton by means of single-exposure speckle photography,” Opt. Commun. 37(5), 326–330 (1981). [CrossRef]

2.

J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1(2), 174–179 (1996). [CrossRef] [PubMed]

3.

P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett. 31(12), 1824–1826 (2006). [CrossRef] [PubMed]

4.

K. Murari, N. Li, A. Rege, X. Jia, A. All, and N. Thakor, “Contrast-enhanced imaging of cerebral vasculature with laser speckle,” Appl. Opt. 46(22), 5340–5346 (2007). [CrossRef] [PubMed]

5.

Z. Wang, S. Hughes, S. Dayasundara, and R. S. Menon, “Theoretical and experimental optimization of laser speckle contrast imaging for high specificity to brain microcirculation,” J. Cereb. Blood Flow Metab. 27(2), 258–269 (2007). [CrossRef] [PubMed]

6.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005). [CrossRef]

7.

H. Cheng, Y. Yan, and T. Q. Duong, “Temporal statistical analysis of laser speckle images and its application to retinal blood-flow imaging,” Opt. Express 16(14), 10214–10219 (2008). [CrossRef] [PubMed]

8.

R. Bi, J. Dong, and K. Lee, “Deep tissue flowmetry based on diffuse speckle contrast analysis,” Opt. Lett. 38(9), 1401–1403 (2013). [CrossRef] [PubMed]

9.

R. Bi, J. Dong, and K. Lee, “Multi-channel deep tissue flowmetry based on temporal diffuse speckle contrast analysis,” Opt. Express 21(19), 22854–22861 (2013). [CrossRef] [PubMed]

10.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988). [CrossRef] [PubMed]

11.

H. Cheng and T. Q. Duong, “Simplified laser-speckle-imaging analysis method and its application to retinal blood flow imaging,” Opt. Lett. 32(15), 2188–2190 (2007). [CrossRef] [PubMed]

12.

S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express 18(14), 14519–14534 (2010). [CrossRef] [PubMed]

13.

P.-A. Lemieus and D. J. Durian, “Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions,” J. Opt. Soc. Am. A 16(7), 1651–1664 (1999). [CrossRef]

14.

A. B. Parthasarathy, W. J. Tom, A. Gopal, X. Zhang, and A. K. Dunn, “Robust flow measurement with multi-exposure speckle imaging,” Opt. Express 16(3), 1975–1989 (2008). [CrossRef] [PubMed]

15.

X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, and D. A. Weitz, “Diffusing-wave spectroscopy in a shear flow,” J. Opt. Soc. Am. B 7(1), 15–20 (1990). [CrossRef]

16.

D. Boas and A. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A 14(1), 192–215 (1997). [CrossRef]

17.

Z. Q. Zhang, I. P. Jones, H. P. Schriemer, J. H. Page, D. A. Weitz, and P. Sheng, “Wave transport in random media: The ballistic to diffusive transition,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(4), 4843–4850 (1999). [CrossRef] [PubMed]

18.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010). [CrossRef]

19.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995). [CrossRef] [PubMed]

20.

L. Wang and S. L. Jacques, http://omlc.ogi.edu/software/mc/.

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(290.1990) Scattering : Diffusion
(290.4210) Scattering : Multiple scattering

ToC Category:
Image Processing

History
Original Manuscript: June 3, 2014
Revised Manuscript: July 22, 2014
Manuscript Accepted: July 26, 2014
Published: August 4, 2014

Virtual Issues
Vol. 9, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Jialin Liu, Hongchao Zhang, Zhonghua Shen, Jian Lu, and Xiaowu Ni, "Quantitatively assessing flow velocity by the slope of the inverse square of the contrast values versus camera exposure time," Opt. Express 22, 19327-19336 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-16-19327


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References

  1. A. Fercher and J. Briers, “Flow visualizaiton by means of single-exposure speckle photography,” Opt. Commun.37(5), 326–330 (1981). [CrossRef]
  2. J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt.1(2), 174–179 (1996). [CrossRef] [PubMed]
  3. P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Opt. Lett.31(12), 1824–1826 (2006). [CrossRef] [PubMed]
  4. K. Murari, N. Li, A. Rege, X. Jia, A. All, and N. Thakor, “Contrast-enhanced imaging of cerebral vasculature with laser speckle,” Appl. Opt.46(22), 5340–5346 (2007). [CrossRef] [PubMed]
  5. Z. Wang, S. Hughes, S. Dayasundara, and R. S. Menon, “Theoretical and experimental optimization of laser speckle contrast imaging for high specificity to brain microcirculation,” J. Cereb. Blood Flow Metab.27(2), 258–269 (2007). [CrossRef] [PubMed]
  6. R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum.76(9), 093110 (2005). [CrossRef]
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